Blood flow through an artery is 80 cm3/s. What will the flow be if the radius of the artery is increased by 10%? Assume that neither the pressure across the artery nor the length of the artery changes. Do not ignore viscosity.
To calculate the change in flow rate when the radius is increased by 10%, we can use the Hagen-Poiseuille equation:
Q = (π*(r^4)*ΔP) / (8*η*L)
where:
Q = flow rate
r = radius of the artery
ΔP = pressure difference across the artery
η = viscosity of the blood
L = length of the artery
Since the pressure difference and the length of the artery are not changing, we can indicate them as constants.
Let's denote the initial radius of the artery as r and the flow rate as Q. When the radius is increased by 10%, the new radius will be 1.1r. Therefore, the new flow rate, Q', can be calculated as:
Q' = (π*((1.1r)^4)*ΔP) / (8*η*L)
Q' = (1.1^4)*(π*(r^4)*ΔP) / (8*η*L)
Q' = 1.464 * Q
Therefore, the flow rate through the artery will increase by approximately 46.4% when the radius is increased by 10%.